1. **State the problem:** Solve the linear equation $2x + 5 = 7$ for $x$. 2. **Formula and rules:** To solve for $x$, isolate the variable by performing inverse operations. Subtract or add terms on both sides to simplify. 3. **Step 1:** Subtract 5 from both sides: $$2x + 5 - 5 = 7 - 5$$ which simplifies to $$2x = 2$$ 4. **Step 2:** Divide both sides by 2 to isolate $x$: $$\frac{2x}{2} = \frac{2}{2}$$ which simplifies to $$x = 1$$ 5. **Final answer:** $x = 1$